The cutting beam may e.g. be in the form of a fluid jet or a laser beam (with regard to waterjet cutting, see e.g. patent specifications U.S. Pat. No. 6,766,216 B2 or U.S. Pat. No. 6,922,605 B1). The cutting beam that forms when leaving the cutting head has no fixed geometry, but represents a kind of dynamic tool, whose impact on the material layer to be cut may vary over time.
For positioning the cutting beam with respect to a cutting line, along which a particular material layer is to be cut, it is known to consider the cross-section of the cutting beam as being circular and invariable. However, this conception restricts the limits of the accuracy with which a material layer can be cut. This model is not suitable for a very accurate cutting.